Solve for $n$. Give an exact answer. $4n+2=6\left(\dfrac13n-\dfrac23\right)$ $n =$
We need to manipulate the equation to get $ n $ by itself. $\begin{aligned} 4n+2 &= 6\left(\dfrac13n-\dfrac23\right) \\\\ 4n+2 &= 2n-4~~~~~~~~~~\gray{\text{Distribute}}\\\\ 4n+2{-2n} &= 2n-4{-2n} ~~~~~~~~~~\gray{\text{Subtract 2n from each side}}\\\\ 2n+2 &= -4~~~~~~~~~~\gray{\text{Combine like terms}}\\\\ 2n+2{-2} &= -4{-2} ~~~~~~~~~~\gray{\text{Subtract 2 from each side}}\\\\ 2n &=-6 ~~~~~~~~~~\gray{\text{Combine like terms}}\\\\ \dfrac{2n}{{2}}&= \dfrac{-6}{{2}}~~~~~~~~~~\gray{\text{Divide each side by 2}} \\\\ n &= {-3} ~~~~~~~~~~\gray{\text{Simplify}}\\\\ \end{aligned}$ The answer: $ n= { -3 }~~~~~~~~$ [Let's check our work!]